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SeasonaleBOUND ACUP Collection
Non-Euclidean Geometry
Fifth Edition
5th edition
By (author):
H.S.M. Coxeter
H.S.M. Coxeter
Imprint:
University of Toronto PressISBN:
9781442653207Product Form:
Electronic book text
Electronic book text
, PDF
English
Audience:
Higher Education
Dec 15, 1965
$84.00 CAD
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Dimensions:
9in x 6 in | 1 grPage Count:
326 pages
University of Toronto Press
MATHEMATICS / Geometry / Non-Euclidean
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This textbook introduces non-Euclidean geometry, and the third edition adds a new chapter, including a description of the two families of 'mid-lines' between two given lines and an elementary derivation of the basic formulae of spherical trigonometry and hyperbolic trigonometry, and other new material.
The name non-Euclidean was used by Gauss to describe a system of geometry which differs from Euclid's in its properties of parallelism. Such a system was developed independently by Bolyai in Hungary and Lobatschewsky in Russia, about 120 years ago. Another system, differing more radically from Euclid's, was suggested later by Riemann in Germany and Cayley in England. The subject was unified in 1871 by Klein, who gave the names of parabolic, hyperbolic, and elliptic to the respective systems of Euclid-Bolyai-Lobatschewsky, and Riemann-Cayley. Since then, a vast literature has accumulated.
The Fifth edition adds a new chapter, which includes a description of the two families of 'mid-lines' between two given lines, an elementary derivation of the basic formulae of spherical trigonometry and hyperbolic trigonometry, a computation of the Gaussian curvature of the elliptic and hyperbolic planes, and a proof of Schlafli's remarkable formula for the differential of the volume of a tetrahedron.
H.S.M. Coxeter (1907-2003) was Professor of Mathematics at the University of Toronto.
"Professor Coxeter's textbook presents the fundamental principles in a clear, readable manner. It should be the standard textbook on non-Euclidean geometry for a long time to come." - Mathematical Gazette
